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DTSTART;TZID=America/Los_Angeles:20211102T123000
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CREATED:20210826T052223Z
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SUMMARY:Counting points in discrete subgroups (Jeff Vaaler\, UT Austin)
DESCRIPTION:We consider the problem of comparing the number of discrete points that belong to a set with the measure (or volume) of the set\, under circumstances where we expect these two numbers to be approximately equal. We start with a locally compact\, abelian\, topological group G. We assume that G has a countably infinite\, torsion free\, discrete subgroup H. But to make the talk easier to follow we will mostly consider the case G = R^N and H = Z^N. If E ⊆ R^N is a subset there are many situations where one expects that the (finite\, positive) number Vol_N (E) is approximately equal to the cardinality |E ∩ Z^N |. We will sketch the proof of a general result that bounds the difference between these quantities. If k is an algebraic number field and k_A is the ring of adeles associated to k\, this general result is useful when G = k_A^N and H = k^N .
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-jeff-vaaler-ut-austin/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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